Espe's Conjecture

This is an early attempt at writing down a half baked idea that needs work.  Stay tuned as I'll edit this as I get ideas.  Thoughts and comment are very welcome.
---  here is my conjecture:


A sufficiently complex system has at least one singularity

These terms need some definition and at present they are still not quantatative enough but here goes

A singularity is an inconsistency or paradox or something that cannot be proved or done in the system itself.

This might be restated along the lines of open versus closed systems, implying there are no closed systems, a closed system being defined as a system with no singularities.

Examples:

Logic - this sentence is false

Cryptography - an electronic system requires some pre-existing trust.  For example, Difffie-Hellman requries some pre-shared secret or it is vulnerable to a man-in-the-middle attack.

General Realitivity - has real singularities inside black holes! 

Math - singularities are called Axioms.

Kurt Godel's Incompleteness Theorem is another example - it might even be a more concise statement of this Conjecture but at this point I'd like to think the conjecture is more general.

You get the idea, if a system is complex enough, it has built in limits, it cannot explain or do things without something from another system or outside actor.